Who is Ballentine and why is he important in the world of quantum mechanics?

[PeterDonis]

all orderings of the entanglement swapping experiment have plausible causal explanations

No, they don't; the case where all the measurements are spacelike separated cannot be explained using your method.

Even for the other cases, where the measurements are timelike or null separated, the "plausible causal explanation" is different for different orderings of the measurements. Which seems highly implausible given that the correlations are exactly the same regardless of the ordering.

 

[vanhees71]

The very fact that the order of measurements in the entanglement-swapping protocol shows that there is no mutual causal influence of these measurements on each other. By definition the cause is always and observer-independently before the effect. That's the fundamental definition of the "arrow of time" underlying all physics (the "causal arrow of time").

In relativistic physics this implies that cause-effect relations can only be between events that are time-like or light-like separated, and that's why in relativsitic QFT local observable-operators must obey the microcausality constraint, i.e., any such operators must commute if their spacetime arguments are space-like separated. That's fulfilled for QED and thus particularly for photon-detection probability-rate densities (the correlation function of the energy density of the em. field). This ensures that QED is a causal theory and thus there cannot be faster-than-light causal influences of one of the measurements on the other, if the measurement events are space-like separated, and thus if the observed correlations are independent of any time-order of the corresponding measurement events there cannot be by definition such a causal influence.

The correlations are due to the preparation of the initial photon state, i.e., the entanglement swapping is possible, because in the beginning, before any measurements are done (and each detector can the earliest register a photon when the wave front has reached this detector, i.e., the earliest after the propagation time of an electromagnetic wave from the source (BBO) to the detector), the photon pairs 1&2 as well as 3&4 are prepared in a maximally entangled Bell state.

 

[Morbert]

@vanhees71 I agree with your position: relativistic quantum theories can be consistently interpreted as local in the sense of events not affecting other spacelike-separated events, but your argument doesn't quite get us there. E.g. Bell would say that your statements do no imply locality in the above sense. They only imply that operations on a system will not affect the statistics of spacelike-separated systems. Relativistic quantum theories still fail Bell's local causality condition. We would need to go further and argue that Bell's local causality condition is not appropriate for determining whether or not, in quantum theories, events can affect spacelike-separated events.

 

[vanhees71]

I avoided this locality discussion, because then I run into danger of a thread ban. I don't know, what Bell means by "locality". For me locality is the assumption of QFT that we describe everything with a Hamilton density consisting of field operators at the same space-time point, have the usual local realization of the Poincare group on the field operators, and that self-adjoint operators representing local observables (like the em. energy-momentum tensor, which contains the description of photon detection, using the usual dipole approximation) obey the microcausality constraints.

Also for me the only consistent interpretation is the minimal statistical interpretation, and there is nothing else than the probabilities. Particularly it does not make sense to ask for a cause of a specific outcome of a measurment on a single system since within this interpretation there is none, but Nature behaves inherently random. Then there are obviously indeed no faster-than-light propagating causal effects, but the strong correlations of measurment results at far distant places when a quantum system is prepared in an entangled state are there due to the preparation of this state, i.e., the "cause" of the correlations is the preparation in the very beginning before any measurements are done. It should also be clear that it doesn't make sense to say a state were local or non-local. What's local are interactions due to the mathematical construction of relativistic, microcausal (in that sense local) QFTs, not states.

I think the big confusion about all this is because of the idea that there should be a cause for each single outcome of a measurement on a quantum system, and then the nebulous meaning of terms like locality or non-locality in the quantum-foundation literature. It seems to be still very hard to accept for some philosophically inclined physicists to accept the "objective randomness" of Nature (or to formulate it more care ful of our observations of Nature), and that after nearly 100 years of quantum theory and Born's break-through with the probability interpretation of the quantum state! On the other hand, I don't see any hint that this assumption is wrong. Particularly all the Bell tests in all kinds of variations, including the space-like separation of measursment/detection events with entangled photons, seem to me only to be consistently interpretible with this assumption of the statistical interpretation.

 

[kurt101]

No, they don't; the case where all the measurements are spacelike separated cannot be explained using your method.

No, they do. I am not sure why you are saying they don't, maybe you are using a different definition of causal than I am.

Where the measurements are done first:
Measurement at 1 causes 2 to receive information of the measurement via entanglement. Measurement 4 causes 3 to receive information of the measurement via entanglement. 2 & 3 have all the information available to decide if 1 & 4 were entangled.

Where measurements are done last:
2 & 3 come together at the BSM (Bell state measurement apparatus) where through the swap 4 gets entangled with 2's partner 1 and likewise 1 gets entangled with 3's partner 4.

Both cases and any mix of the cases can all be considered causal in nature.

 

[kurt101]

I don't know, what Bell means by "locality".

FWIW, I don't know if you are just saying this to make a point, but Bell is using the definition of locality used by everyone else outside of QFT (at least your version of QFT). If I read a QM paper and it used locality in the way you are using it and did not explicitly tell me, I would be extremely confused. It would at least be helpful to give it some extra context so we knew when you are talking about your versions of QFT locality versus the common definition. Is there such a term you use to avoid confusion?

 

[PeterDonis]

maybe you are using a different definition of causal than I am

The standard definition of "causal", as @vanhees71 has pointed out, requires an invariant time ordering of cause before effect. The time ordering of spacelike separated events is not invariant, so they cannot be causally connected using that definition.

If you are using a different definition of "causal", please give a reference to back it up.

 

[PeterDonis]

Where the measurements are done first:

Where measurements are done last:

If the events are spacelike separated, neither of these are true; the time ordering is frame dependent, and standard relativity says that no physical effect can depend on something that is frame dependent; all the physics must be contained in invariants.

 

[kurt101]

The standard definition of "causal", as @vanhees71 has pointed out, requires an invariant time ordering of cause before effect. The time ordering of spacelike separated events is not invariant, so they cannot be causally connected using that definition.

If you are using a different definition of "causal", please give a reference to back it up.

What would you call the dependency between two entangled photons? Using the definition of "casual" from the Oxford dictionary I would consider this dependency causal. Measuring one photon affects the measurement of the other photon.

 

[PeterDonis]

What would you call the dependency between two entangled photons?

Entanglement. Whether that counts as a "causal" connection is one of the key unresolved issues in QM interpretation.

Measuring one photon affects the measurement of the other photon.

If the measurements are spacelike separated, their time ordering is frame dependent, which means their cause and effect ordering is frame dependent. It is of course logically possible to extend one's definition of "causality" to include this case: but whether or not that is justified, and whether or not one is willing to accept all the consequences of that choices, is a matter of opinion. There is no generally accepted resolution to these issues.

 

[vanhees71]

I think there's nothing unsolved, and of course QM, which is non-relativistic, is not the right theory to discuss the issue, because for that you need a relativistic model, and the only successful relstivistic quantum theory is relativistic QFT.

What entanglement describes are correlations between the outcome of measurements. They are "caused" by the preparation of the measured system in the state. In general the operational definition of quantum state is that it describes a preparation procedure, e.g., the emission of an entangled photon pair from a BBO crystal due to parametric down conversion.

All observed facts about entanglement, including all the predicted effects like teleportation, entanglement swapping, delayed-choice erasing, etc. etc. are confirmed by highly accurate experiments (Nobel Prize of 2022). There's nothing unsolved here! It's now in the realm of engineering. Universities of Applied Sciences now develop curricula for quantum informatics!

 

[Fra]

The order doesn't matter, because there's no need for a causal effect of one measurement on the other.

This fact does not mean that nature itself has no causal internal relationships at all. I think THAT is somerhing many will not accept.

My opinion is that its the nature of causality that QM challenges. In Classical mechanics we tend to have a "mechanical view" of causal chains and something in 3D need to basically "poke" something to provide a mechanism.

In QM it seems to me that causation is more easily understood as a game of expectations. Any players behaviour is ultimately governed by its own expectations. The "poking" going on as in the space of expectations of a player(could be a detector)
This is IMO an intuitive way to understand HOW the hidden variable provides a mechanism for CORRELATIONS of outcomes but NOT for the actual outcome!

/Fredrik

 

[Fra]

I think there's nothing unsolved,

....

What entanglement describes are correlations between the outcome of measurements. They are "caused" by the preparation of the measured system in the state. In general the operational definition of quantum state is that it describes a preparation procedure,

I agree with all, but what I think is missing is a deeper understanding of what we describe well but does not understand well. This is what i label nature of causality.

/Fredrik

 

[vanhees71]

Then the question is, what you define as "understanding (Nature?) well". We have a pretty well formulated theory, Q(F)T, that describes almost all (everything except gravitation as far as we know) phenomena in accordance with all empirical evidence. What do you think is "lacking in understanding" then?

 

[Fra]

What do you think is "lacking in understanding" then?

Conceptually: The theoretical perspective of an "inside observer" AND how that would comply to the "external observer" perspective. Worth noting that any real observer is always and inside observer. Current perspective is an abstraction and a limiting case.

A bonus I expect from such insight, is that we will be able to reduce the number of "free" or "fine tuned" parameters in our current description.

/Fredrik

 

[bhobba]

Why don't you start by asking them back, "What is a field?"

A theorem called the no interaction theorem says that in relativity, particles left to themselves will never interact.

But we know they often do. To get around this, fields are postulated to exist. Wigner showed they all must be tensors. In fact, by starting with a tensor type, it is often possible to write down the equations of the field with just a little bit of other knowledge, e.g.,

https://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

We know from Noether's Theorem they have momentum and energy - properties associated usually with real things. Because of this, we think fields are real but mathematically described by tensors. What they are is anyone's guess.

Regarding Quantum Field Theory, Weinberg often mentioned what he called a folk theorem. There is no rigorous proof, but physicists generally believe it is true. It says any theory that includes Special Relativity and Quantum Mechanics, plus the cluster decomposition property, will look like a Quantum Field theory at large enough distances.

https://www.arxiv-vanity.com/papers/hep-th/9702027/

Particles (very real things) are like knots in these fields. Therefore, we think of them as real and know how to describe them mathematically, but just like classical fields, what they are is anyone's guess.

Thanks
Bill

 

[bhobba]

Is Ballentine really good at explaining this sort of thing? Thanks for all your very helpful replies.

Ballentine, in my opinion, is THE book on quantum mechanics.

But you have to build up to it:


Thanks
Bill

 

[apostolosdt]

l’ll be naively honest: Until I became a member of these Forums, l had never heard of Ballentine, or his RMP article or his QM book for that matter. Of course that has no weight on his work or on other members’ opinion. But it’s kind of strange. One possible explanation might be that I never worked with people who were interested in interpretations of quantum mechanics—I was more of the sort “Shut up and do your Feynman diagrams.”

 

[vanhees71]

A theorem called the no interaction theorem says that in relativity, particles left to themselves will never interact.

But we know they often do. To get around this, fields are postulated to exist. Wigner showed they all must be tensors. In fact, by starting with a tensor type, it is often possible to write down the equations of the field with just a little bit of other knowledge, e.g.,

https://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

We know from Noether's Theorem they have momentum and energy - properties associated usually with real things. Because of this, we think fields are real but mathematically described by tensors. What they are is anyone's guess.

The "real things" are observables, in relativistic QFTs local ones, represented by corresponding local operators, built with help of the fields. In the case of gauge theories, of course only gauge-covariant local field operators can represent such observables.

That's often not clearly mentioned, particularly not in non-relativistic QM in the semiclassical approximation, i.e., with the electrons (or other charged particles) "quantized" and the em. field kept classical. There's a lot of confusion in the textbook literature about this. Even recently there was a paper about the confusion related to the Landau problem (charged particle in a homogeneous magnetic field). All this is, of course, clarified. A good treatment can be found in the textbook by Cohen-Tannoudji (Complement H III in Vol. 1 of Cohen-Tannoudji, Diu, Laloe, Wiley 2020).

Regarding Quantum Field Theory, Weinberg often mentioned what he called a folk theorem. There is no rigorous proof, but physicists generally believe it is true. It says any theory that includes Special Relativity and Quantum Mechanics, plus the cluster decomposition property, will look like a Quantum Field theory at large enough distances.

https://www.arxiv-vanity.com/papers/hep-th/9702027/

Particles (very real things) are like knots in these fields. Therefore, we think of them as real and know how to describe them mathematically, but just like classical fields, what they are is anyone's guess.

"Particles" are asymptotic free Fock states with "particle number" 1. Particles are not an easy concept in QFT! Of course Weinberg is always the right address to clarify conceptional questions (at least concerning QFT ;-)).

 

[bhobba]

l had never heard of Ballentine, or his RMP article or his QM book for that matter.

Ballentine is famous for years ago publishing a paper on the statistical interpretation:

https://www.unicamp.br/~chibeni/textosdidaticos/ballentine-1970.pdf

His book is well respected here because it integrates graduate-level QM with his favoured statistical interpretation.

As a personal comment, I learned QM from Dirac and von Neumann. I got sidetracked into investigating Rigged Hilbert Spaces. Then I read Ballentine, and it was a revelation - all was much clearer. I have since read many other books, some of which are very good, like Weinberg, but others were not to my taste.

You are correct. Ballentine is well thought of by many people here (not all, though).

Thanks
Bill

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